Red Brand Canners (Rbc)

Case 2: Red Brand Canners (RBC)

Executive Summary

Red Brand Canners would like to determine production levels for its tomato products this season in order to maximize profits. It is my understanding that each product is sold by the case, and that a case of canned whole tomatoes takes 18 pounds of tomatoes, a case of tomato juice takes 20 pounds, and a case of tomato paste takes 25 pounds. Each product is made up of Grade A tomatoes (Average Quality: 9) and/or Grade B tomatoes (Average Quality: 5).

Physical production limitations include the supply of Grade A tomatoes (600,000) and the supply of Grade B tomatoes (2,400,000). According to Myers’ demand forecasts, production should be limited to 14.4 million pounds for whole canned tomatoes, one million pounds for tomato juice, and two million pounds for tomato paste. In addition, the quality for the whole tomatoes must be at least 8, while the quality for tomato juice must be at least 6.

We have been given the opportunity to look at the production requirements for these three products, and to analyze the situation in Red Brand Canner’s best interest. By assuming that the production requirements and contribution margins remain constant, I was able to use Excel to solve this linear programming problem and maximize profit for the company.

Recommendations

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Proposed Production

Grade A (lbs) Grade B (lbs) Profit

Canned Tomatoes 525,000 175,000 $57,540

Tomato Juice 75,000 225,000 $19,800

Tomato Paste 0 2,000,000 $148,000

Total 600,000 2,400,000 $225,340

Questions

1. The decision variables in this linear programming model cover three products: canned whole tomatoes, tomato juice, and tomato paste. Each product can be made from a combination of Grade A tomatoes and Grade B tomatoes. This effectively means there are six decision variables (2 types of tomatoes x 3 types of products)....